Netherlands · Year 12 · Practice Sheet 9

1. 1.

   A force of 81 N moves an object 21 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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2. 2.

   A body starts at 12 m/s and accelerates at 2 m/s² for 5 s. Find its final velocity.

   Formula:Kinematics (v = u + at)

   $v = u + at$

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3. 3.

   An object with initial velocity 14 m/s accelerates at 2.2 m/s² for 4 s. Find the distance travelled.

   Formula:Kinematics (s = ut + ½at²)

   $s = ut + \tfrac{1}{2}at^2$

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4. 4.

   Find the momentum of a 24 kg object moving at 25 m/s.

   Formula:Momentum

   $p = mv$

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5. 5.

   Find the population standard deviation of: 16, 3, 13, 9, 15 (to 2 d.p.).

   Formula:Standard Deviation (Population)

   $\sigma = \sqrt{\dfrac{\sum (x - \bar{x})^2}{n}}$

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6. 6.

   Find the sum of the first 20 terms of an arithmetic series with first term a = 11 and common difference d = 8.

   Formula:Sum of an Arithmetic Series

   $S_n = \tfrac{n}{2}\left(2a + (n-1)d\right)$

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7. 7.

   A triangle has sides a = 8 cm and b = 5 cm with an included angle C = 90°. Find its area (to 2 d.p.).

   Formula:Area of a Triangle (Sine Rule)

   $A = \tfrac{1}{2} ab\sin C$

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8. 8.

   In a triangle, a = 18, b = 13 and the included angle C = 50°. Find side c (to 2 d.p.).

   Formula:Cosine Rule

   $c = \sqrt{a^2 + b^2 - 2ab\cos C}$

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9. 9.

   €1,200 is invested at 4% compound interest per annum for 4 years. Find the final amount (to 2 d.p.).

   Formula:Compound Interest

   $A = P\left(1 + \dfrac{r}{100}\right)^{t}$

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10. 10.

    A population of 4,800 grows 10% per year. Find its size after 3 years (nearest whole number).

    Formula:Exponential Growth

    $N = N_0 (1 + r)^{t}$

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11. 11.

    A device runs at 214 V drawing 9.7 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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12. 12.

    Find the momentum of a 24 kg object moving at 30 m/s.

    Formula:Momentum

    $p = mv$

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13. 13.

    Find the gravitational potential energy of a 40 kg object raised 39 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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14. 14.

    Find the population standard deviation of: 6, 7, 16, 4, 20 (to 2 d.p.).

    Formula:Standard Deviation (Population)

    $\sigma = \sqrt{\dfrac{\sum (x - \bar{x})^2}{n}}$

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15. 15.

    In a triangle, a = 6, b = 9 and the included angle C = 70°. Find side c (to 2 d.p.).

    Formula:Cosine Rule

    $c = \sqrt{a^2 + b^2 - 2ab\cos C}$

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16. 16.

    A body starts at 18 m/s and accelerates at 1.5 m/s² for 3 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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17. 17.

    A force of 109 N moves an object 30 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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18. 18.

    A cone has base radius 10 cm and height 23 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cone

    $V = \tfrac{1}{3} \pi r^2 h$

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19. 19.

    A device runs at 198 V drawing 0.9 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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20. 20.

    A 12 kg object moves at 10 m/s. Find its kinetic energy.

    Formula:Kinetic Energy

    $KE = \tfrac{1}{2} m v^2$

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